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Skills available for Wales year 9 maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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Curriculum for Wales: Progression step 4, Year 9 Curriculum for Wales: Progression step 4, Year 9
National Curriculum: Key Stage 3 Year 9 National Curriculum: Key Stage 3 Year 9

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1 Developing numerical reasoning

1.1 Identify processes and connections
- 1.1.1 transfer mathematical skills across the curriculum in a variety of contexts and everyday situations
- 1.1.2 select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks
- 1.1.3 prioritise and organise the relevant steps needed to complete the task or reach a solution
- 1.1.4 choose an appropriate mental or written strategy and know when it is appropriate to use a calculator
- 1.1.5 use a scientific calculator to carry out calculations effectively and efficiently using the available range of function keys
- 1.1.6 identify, measure or obtain required information to complete the task from a range of sources, including text
- 1.1.7 select appropriate mathematics and techniques to use
- 1.1.8 estimate and visualise size when measuring and use the correct units
- 1.1.9 develop and evaluate mathematical strategies and ideas creatively
- 1.1.10 consider connections between mathematical skills and contextualise these within extended tasks
1.2 Represent and communicate
- 1.2.1 explain results and procedures precisely using appropriate mathematical language
- 1.2.2 refine methods of recording calculations
- 1.2.3 use appropriate notation, symbols and units of measurement, including compound measures
- 1.2.4 select and construct appropriate charts, diagrams and graphs with suitable scales
- 1.2.5 interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading
- 1.2.6 evaluate different forms of recording and presenting information, taking account of the context and audience
- 1.2.7 generalise in words, and use algebra, to describe patterns that arise in numerical, spatial or practical situations
  - Write a linear equation from a table (9-T.15)
  - Write a linear equation: word problems (9-T.16)
1.3 Review
- 1.3.1 select and apply appropriate checking strategies
- 1.3.2 interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible
- 1.3.3 verify and justify results or solutions, including discussion on risk and chance where relevant
- 1.3.4 interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data
- 1.3.5 draw conclusions from data and recognise that some conclusions may be misleading or uncertain
  - Interpret charts to find mean, median, mode and range (9-EE.2)
- 1.3.6 justify numerical and algebraic results, making appropriate connections
- 1.3.7 explain and justify strategies, methods, reasoning and conclusions in a variety of different ways, including orally, graphically, in writing (both in mathematical notation and without), and using appropriate digital literacy equipment
- 1.3.8 appreciate the difference between mathematical explanation and experimental evidence; recognise inconsistencies and bias
  - Identify representative, random and biased samples (9-EE.8)
  - Experimental probability (9-FF.4)

2 Using number skills

2.1 Use number facts and relationships
- 2.1.1 use known facts to derive others, e.g. use 7 x 6 to derive 42 ÷ 0.0006
- 2.1.2 use powers and understand the importance of powers of 10, and its application in standard form, e.g. 2? x 2? = 2 to the 14th power
  - Convert between ordinary numbers and standard form (9-G.1)
  - Compare numbers written in standard form (9-G.3)
- 2.1.3 show awareness of the need for standard form and its representation on a calculator
- 2.1.4 represent standard form on a calculator
- 2.1.5 multiply, divide and use brackets with powers
  - Evaluate expressions using properties of indices (9-F.13)
- 2.1.6 write a number as a product of its prime factors in index form
  - Prime factorisation (9-A.2)
2.2 Fractions, decimals, percentages and ratio
- 2.2.1 use equivalence of fractions, decimals, percentages and ratio to select the most appropriate for a calculation
- 2.2.2 use, interpret and calculate with different representations of fractions, e.g. mixed numbers and improper fractions
- 2.2.3 calculate a percentage increase or decrease
  - Percent of change (9-J.13)
  - Percent of change: word problems (9-J.14)
- 2.2.4 express one quantity as a percentage of another, including those given in different units
- 2.2.5 use ratio and proportion to calculate quantities, including cases where the 'total' is not given
2.3 Calculate using mental and written methods
- 2.3.1 use efficient written methods to add and subtract numbers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places
- 2.3.2 multiply and divide whole numbers and decimals
- 2.3.3 use the order of operations including brackets and powers
  - Evaluate numerical expressions involving integers (9-C.12)
  - Evaluate numerical expressions involving rational numbers (9-E.13)
- 2.3.4 use the four operations in multistep calculations involving negative numbers, using mental and written methods
2.4 Estimate and check
- 2.4.1 make and justify estimates and approximations of calculations
- 2.4.2 choose the appropriate degree of accuracy to present answers
2.5 Manage money
- 2.5.1 calculate using foreign money and exchange rates
- 2.5.2 understand the risks involved in different ways of saving and investing
- 2.5.3 describe why insurance is important and understand the impact of not being insured

3 Using measuring skills

3.1 Length, weight/mass, capacity
- 3.1.1 find circumferences of circles and perimeters of semicircles and quadrants
  - Circumference of circles (9-Y.4)
- 3.1.2 derive and use Pythagoras' theorem
- 3.1.3 make links between speed, distance and time
- 3.1.4 understand and use a variety of compound measures, including speed and density
- 3.1.5 define upper and lower bounds of discrete measurements
- 3.1.6 recognise that there are different considerations for continuous data
3.2 Time
- 3.2.1 use timetables and time zones to plan a journey
3.3 Temperature
- 3.3.1 convert temperatures between appropriate temperature scales
3.4 Area and volume Angle and position
- 3.4.1 find areas of circles, semicircles and quadrants
  - Circumference of circles (9-Y.4)
- 3.4.2 calculate surface areas of cubes and cuboids
  - Surface area of prisms and cylinders (9-Y.13)
- 3.4.3 calculate volumes of prisms and cylinders
  - Volume of prisms and cylinders (9-Y.11)
- 3.4.4 calculate angles on parallel lines
  - Transversals of parallel lines: name angle pairs (9-W.8)
- 3.4.5 calculate interior and exterior angles of polygons
  - Find missing angles in triangles and quadrilaterals (9-W.2)
  - Interior angles of polygons (9-W.4)
- 3.4.6 draw the relative position of objects given the bearing of one from the other
- 3.4.7 apply understanding of bearings and scale to interpret maps and plans, and to create plans and drawings to scale
  - Scale drawings: word problems (9-H.9)

4 Using geometry skills

4.1 Shape
- 4.1.1 recognise similar shapes and calculate the size of missing sides with whole number scale factor
  - Identify congruent figures (9-AA.1)
  - Side lengths and angle measures of similar figures (9-AA.8)
- 4.1.2 explore properties of shapes that tessellate
4.2 Construction
- 4.2.1 select and use appropriate equipment to draw triangles when given sufficient angles and sides
  - Construct an equilateral triangle or regular hexagon (9-CC.5)
4.3 Movement
- 4.3.1 rotate shapes about the origin
  - Rotations: graph the image (9-Z.7)
  - Rotations: find the coordinates (9-Z.8)
- 4.3.2 describe rotations about the origin
  - Rotations: graph the image (9-Z.7)
  - Rotations: find the coordinates (9-Z.8)
- 4.3.3 enlarge a shape around a centre where the scale factor is positive
- 4.3.4 explore locus where the path is a given distance from a point, line or shape

5 Using algebra skills

5.1 Number sequences
- 5.1.1 use the nth term rule to determine whether a number is in a sequence
  - Evaluate variable expressions for arithmetic sequences (9-O.6)
- 5.1.2 determine the position number of a given term
- 5.1.3 distinguish between a linear and non-linear sequence
  - Identify arithmetic and geometric sequences (9-O.1)
5.2 Expressions and formulae
- 5.2.1 show and use rules that involve the multiplication, division and use of brackets with index variables
- 5.2.2 simplify expressions including expansion of a single bracket, including a(b + c) + d(e + f), and double brackets
- 5.2.3 factorise algebraic expressions of two or more terms into a single bracket where there is one common factor
  - Factors of linear expressions (9-P.12)
- 5.2.4 rearrange formulae involving two or more variables
  - Rearrange multi-variable equations (10-F.18)
5.3 Functions and graphs
- 5.3.1 examine features of linear functions, read an intercept from a graph, and recognise positive and negative gradients
- 5.3.2 recognise the impact of the coefficient of x on the gradient of the line
  - Find the gradient and y-intercept of a linear equation (9-T.8)
5.4 Equations and inequalities
- 5.4.1 construct and solve equations that include brackets () and a() + b()
- 5.4.2 construct and solve equations where the variable appears on both sides of the equals sign
  - Solve equations with variables on both sides (9-Q.11)
- 5.4.3 solve equations by trial and improvement and justify the solution
  - Which x satisfies an equation? (9-Q.1)
  - Solve two-step equations: word problems (9-Q.7)
- 5.4.4 express situations as inequalities
- 5.4.5 solve inequalities and show the solutions on a number line
- 5.4.6 construct and interpret information graphs that relate to a variety of situations, e.g. running a bath

6 Using data skills

6.1 Collect and record data Present and analyse data Interpret results
- 6.1.1 test hypotheses, making decisions about how best to record and analyse the information from large data sets
  - Choose the best type of graph (9-DD.15)
  - Identify representative, random and biased samples (9-EE.8)
- 6.1.2 construct and interpret graphs and diagrams (including pie charts) to represent discrete or continuous data, with the learner choosing an appropriate scale
- 6.1.3 select and justify statistics most appropriate to the problem considering extreme values (outliers)
- 6.1.4 examine results critically, select and justify choice of statistics recognising the limitations of any assumptions and their effect on the conclusions drawn
- 6.1.5 use appropriate mathematical instruments and methods to construct accurate drawings
- 6.1.6 find the mean, median, mode and range from grouped frequency tables and explain why it is an estimate
6.2 Probability
- 6.2.1 use the sum of all probabilities is 1 – simple cases, e.g. rolling a dice P (not 6)
  - Probability of simple events (9-FF.1)
  - Probability of mutually exclusive events and overlapping events (9-FF.3)
- 6.2.2 recognise that practice is different from theory and that repeated experiments may give different results
  - Experimental probability (9-FF.4)
- 6.2.3 understand that reliability/stability increases with a greater number of trials
- 6.2.4 construct a sample space diagram and a two way table.
  - Compound events: find the number of outcomes (9-FF.7)

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1 Developing numerical reasoning

1.1 Identify processes and connections

1.1.1 transfer mathematical skills across the curriculum in a variety of contexts and everyday situations

1.1.2 select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks

1.1.3 prioritise and organise the relevant steps needed to complete the task or reach a solution

1.1.4 choose an appropriate mental or written strategy and know when it is appropriate to use a calculator

1.1.5 use a scientific calculator to carry out calculations effectively and efficiently using the available range of function keys

1.1.6 identify, measure or obtain required information to complete the task from a range of sources, including text

1.1.7 select appropriate mathematics and techniques to use

1.1.8 estimate and visualise size when measuring and use the correct units

1.1.9 develop and evaluate mathematical strategies and ideas creatively

1.1.10 consider connections between mathematical skills and contextualise these within extended tasks

1.2 Represent and communicate

1.2.1 explain results and procedures precisely using appropriate mathematical language

1.2.2 refine methods of recording calculations

1.2.3 use appropriate notation, symbols and units of measurement, including compound measures

1.2.4 select and construct appropriate charts, diagrams and graphs with suitable scales

1.2.5 interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading

1.2.6 evaluate different forms of recording and presenting information, taking account of the context and audience

1.2.7 generalise in words, and use algebra, to describe patterns that arise in numerical, spatial or practical situations

1.3 Review

1.3.1 select and apply appropriate checking strategies

1.3.2 interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible

1.3.3 verify and justify results or solutions, including discussion on risk and chance where relevant

1.3.4 interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data

1.3.5 draw conclusions from data and recognise that some conclusions may be misleading or uncertain

1.3.6 justify numerical and algebraic results, making appropriate connections

1.3.7 explain and justify strategies, methods, reasoning and conclusions in a variety of different ways, including orally, graphically, in writing (both in mathematical notation and without), and using appropriate digital literacy equipment

1.3.8 appreciate the difference between mathematical explanation and experimental evidence; recognise inconsistencies and bias

2 Using number skills

2.1 Use number facts and relationships

2.1.1 use known facts to derive others, e.g. use 7 x 6 to derive 42 ÷ 0.0006

2.1.2 use powers and understand the importance of powers of 10, and its application in standard form, e.g. 2? x 2? = 2 to the 14th power

2.1.3 show awareness of the need for standard form and its representation on a calculator

2.1.4 represent standard form on a calculator

2.1.5 multiply, divide and use brackets with powers

2.1.6 write a number as a product of its prime factors in index form

2.2 Fractions, decimals, percentages and ratio

2.2.1 use equivalence of fractions, decimals, percentages and ratio to select the most appropriate for a calculation

2.2.2 use, interpret and calculate with different representations of fractions, e.g. mixed numbers and improper fractions

2.2.3 calculate a percentage increase or decrease

2.2.4 express one quantity as a percentage of another, including those given in different units

2.2.5 use ratio and proportion to calculate quantities, including cases where the 'total' is not given

2.3 Calculate using mental and written methods

2.3.1 use efficient written methods to add and subtract numbers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places

2.3.2 multiply and divide whole numbers and decimals

2.3.3 use the order of operations including brackets and powers

2.3.4 use the four operations in multistep calculations involving negative numbers, using mental and written methods

2.4 Estimate and check

2.4.1 make and justify estimates and approximations of calculations

2.4.2 choose the appropriate degree of accuracy to present answers

2.5 Manage money

2.5.1 calculate using foreign money and exchange rates

2.5.2 understand the risks involved in different ways of saving and investing

2.5.3 describe why insurance is important and understand the impact of not being insured

3 Using measuring skills

3.1 Length, weight/mass, capacity

3.1.1 find circumferences of circles and perimeters of semicircles and quadrants

3.1.2 derive and use Pythagoras' theorem

3.1.3 make links between speed, distance and time

3.1.4 understand and use a variety of compound measures, including speed and density

3.1.5 define upper and lower bounds of discrete measurements

3.1.6 recognise that there are different considerations for continuous data

3.2 Time

3.2.1 use timetables and time zones to plan a journey

3.3 Temperature

3.3.1 convert temperatures between appropriate temperature scales

3.4 Area and volume Angle and position

3.4.1 find areas of circles, semicircles and quadrants

3.4.2 calculate surface areas of cubes and cuboids

3.4.3 calculate volumes of prisms and cylinders

3.4.4 calculate angles on parallel lines

3.4.5 calculate interior and exterior angles of polygons

3.4.6 draw the relative position of objects given the bearing of one from the other

3.4.7 apply understanding of bearings and scale to interpret maps and plans, and to create plans and drawings to scale

4 Using geometry skills

4.1 Shape